The present invention relates to an image reconstruction method and X-ray CT (computed tomography) apparatus, and more particularly to an image reconstruction method and X-ray CT apparatus capable of providing an image reduced in artifacts caused by a scan plane tilted with respect to a rotation plane when a multi-row detector is employed.
FIG. 6 is an prior art diagram showing an image reconstruction method described in Japanese Patent Application Laid Open No. H8-187241.
An X-ray tube 11 and an X-ray detector 53 rotate around a center of rotation IC to collect data at different view angles. The scan plane is defined as an x-y plane.
Image production is basically conducted as follows:    (0) The pixel values for all pixel points g(x, y) in an image reconstruction plane are initialized to zero;    (1) A channel i is determined which detects an X-ray passing through a pixel point g(x, y) in the image reconstruction plane P at a view angle β;    (2) Data of the channel i is added to the pixel value of the pixel point g(x, y);    (3) (1) and (2) are repeated for each view angle β within a required angular range (e.g., 360°) to obtain the pixel value for the pixel point g(x, y); and    (4) (0)–(3) are repeated for every pixel point g(x, y) in the image reconstruction plane P.
The channel i can be uniquely determined once an angle γ that the X-ray passing through the pixel point g(x, y) forms with a center axis Bc of the X-ray beam is known.
The angle γ can be calculated by the following equation:
      γ    =          arc      ⁢                          ⁢      tan      ⁢              {                  t                      D            +            s                          }              ,                where                    s=x·cos β−y·sin β, and            t=x·sin β−y·cos βwhere x, y, β, s and t are positive in a direction indicated by arrows shown in FIG. 6; the distance from the X-ray tube 11 to the center of rotation IC is represented by D; s denotes the distance from the foot of the perpendicular dropped from the pixel point g toward the center axis Bc of the X-ray beam, to the center of rotation; and t denotes the length of the perpendicular dropped from the pixel point g toward the center axis Bc of the X-ray beam.                        
FIG. 7 is an explanatory diagram showing which detector row the X-ray passing through the pixel point g(x, y) enters when a multi-row detector 13 having more than one detector row is employed. The direction normal to the x-y plane, i.e., a detector row direction, is referred to as a z-axis direction. It should be noted that FIG. 7 is a view from a direction orthogonal to the center axis Bc of the X-ray beam.
The larger the width of the multi-row detector 13 in the z-axis direction, i.e., in the row direction, the greater the tilt of the scan plane with respect to the rotation plane.
Conventionally, the tilt is ignored and an image of the image reconstruction plane P is produced by selecting an m-th detector row corresponding to the z-axis position of the image reconstruction plane P and using data of the m-th detector row.
However, the X-ray passing through the pixel point g(x, y) shown in FIG. 7 enters a j-th detector row, instead of the m-th detector row. Thus, there has been a problem that this results in artifacts.
That is, there has been a problem that artifacts (cone angle artifacts) appear which are caused by a scan plane tilted with respect to the rotation plane when a multi-row detector is employed.